\begin{savequote}[8cm]
%Everyone here has the sense that right now is one of those moments when we are
%influencing the future.
%\qauthor{Steve Jobs}
The feeling is less like an ending than just another starting point.
\qauthor{Chuck Palahniuk}
\end{savequote}

\chapter{Reflections and outlook}
\label{ch:conclusion}
The general public as well as academic scholars believed that the Internet, as
many other historical breakthroughs in human communication technology,
would turn the entire planet into a ``Global Village'', where space is
irrelevant and geographic distances do no longer matter. This thesis is inspired
by  an important and contrasting idea: individuals are affected by spatial
proximity and geographic factors in their online social interactions.  

This dissertation has supported this thesis with a body of work
largely made possible by two increasingly important trends: the advent of the mobile
Web and the popularity of online social networks. As users access
online services through 
location-sensing devices, service providers gather data about where individuals
are located and where they go, together with information about their social
interactions. This exposes the spatial properties of the social
connections arising on the Web, generating possibilities for study and analysis;
also, this opens the door for a wide new range of systems and
application. 

This dissertation has explored both these threads: we first focussed on
studying and understanding how spatial and social properties of online social
services are related to each other. We then proposed new ways of taking
advantage of spatial data to provide, respectively, better link prediction
engines and better caching of content in planetary delivery networks.

\section{Summary of contributions}
When considering the effect that geographic constraints could have on online
social services, the properties of their social graphs need to be reconsidered
taking into account the
metric space where individuals are embedded. Thus, in Chapter~\ref{ch:structure}
we adopted a  methodology that treats the social graph as a spatial
network, associating a geographic distance to every social connection.  We 
observed that users with more connections appear  less constrained by geographic
distance and, using two different randomised null models, we assessed
how the observed properties could not arise from social or spatial factors
alone: both dimensions ought to be jointly considered.

These findings were revisited in Chapter~\ref{ch:model}, where we 
analysed the temporal growth of an  online social network with respect to its
spatial properties. We found evidence that the creation of new links can be
reproduced by a gravitational attachment model, where new connections are 
created with nodes that are either already well connected or spatially close.
This mechanism combines together a purely social property, the number of
connections a user already has, with a purely spatial measure, the geographic
distance between users.
To our surprise, we found that only social factors seem to drive triadic closure,
which appears largely unaffected by distance. We combined these
observations to define a new model of network growth that reproduces
the spatial and social properties observed in real data.

The study of the spatial properties of online social services has offered new
insights about user behaviour, inspiring new systems and applications. Hence, we have
covered and discussed two practical cases where spatial properties of online
social networks are explicitly used, respectively, to enhance friend suggestion
engines and to improve caching policies used in distributed content delivery
networks. 

In Chapter~\ref{ch:prediction} we described how friend prediction
systems can rely on the places that users visit to find suitable candidate for
predictions, reducing the overall prediction space and still covering a large
fraction of future connections.  We have shown that  the properties of the
places that two users share can be used to build prediction features; we have
proposed and evaluated a supervised learning approach which achieves high
performance. 

We discussed a different application in Chapter~\ref{ch:caching}:
adopting caching policies in content delivery networks to serve items over the
planet. Our key idea is that content consumption is fostered by users sharing
items over online social networks: as their social connections are constrained by space, we can
understand which items are popular on a geographically local scale by tracking
their spreading by means of social cascades. Again, we have shown how exploiting
the spatial properties of online social interactions can effectively improve
delivery performance, using a trace-driven simulation of global content
requests.

Returning to our initial thesis, we feel that geography and space affect online
social interaction in a strong and straightforward way: users will want to
connect to other individuals who are ``popular'', regardless of where those
users are located, or to other individuals who are ``close'', even though they
might be relatively unheard of. In other words, the mere fact of being spatially close to someone else greatly increases
how interesting, or socially attractive, that individual is. At the same time,
other factors such as homophily and transitivity appear less affected by
space; instead, they might be influenced by properties such as similarity, user
preferences and other measures of like-mindedness. Overall, it seems that being
in proximity, either in the geographic sense or by sharing common interests,
is what brings new social connections to life.

In summary, we believe that the three main spatial properties that online social
services exhibit are the likelihood of friendship connection that decreases as
an inverse power of spatial distance, strong correlations between
spatial properties and node degree, and the lack of spatial constraints on social
triads.   These properties may hold for other 
social systems embedded in space and are likely to strongly influence other
characteristics commonly observed in social graphs, such as community structure
and the properties of navigable network paths.

\section{Future directions}
% Future directions
From these considerations, geographic proximity arises as yet another factor that
brings individuals to connect to each other. This simple observation also
suggests many possibilities for future work.

First, a key question is whether the effect of spatial distance can be
introduced beyond the gravitational attachment process. Even though our new
model reproduces some social and spatial properties observed in the real graphs,
it may fail to replicate  many other characteristics such as community
structure, transitivity and small-world behaviour that are observed in
online services. Thus, two different but related threads of work need to
be carried out: the analysis of the spatial properties of these phenomena,
in order to understand how geographic distance influences
different facets of social networks, and the extension of the network growth
model to take into account these new findings.

% Community detection over space?
In fact, another property of online social networks likely to be strongly
influenced by distance is community structure. The existence of social groups
is as important as the effect of spatial distance to fully understand how
individuals establish social ties. Since geographic proximity fosters
connections, large and dense communities might be more likely to arise between
individuals close to each other rather than far apart. Recent results on mobile
phone interactions confirm that communities are constrained by geography and
only groups with more than 30 members gradually lose these spatial limitations,
spanning wider areas~\cite{OAG11:geogroups}.  In Chapter~\ref{ch:model} we
jointly  considered social and spatial factors to reproduce the properties
observed in real online social networks: this study could be further extended
to understand whether our model reproduces the communities present in real
scenarios and, if it fails, what modifications would be needed to capture how
real social communities are created over space.

% Mobility and social patterns
Then, on a broader scope, the close relationship  between  how users create new
friendship ties and how users move across places has to be explored.  As
discussed in Chapter~\ref{ch:prediction},  the places visited by users can
reveal which new social connections are likely to arise in the future. This
relationship can be reversed with equally promising results, as users can be
influenced by their friends when choosing which new places to visit.  By
simultaneously  considering these two influences, from places to social
connections and from social connections to places,  there is the potential to
expand our understanding of each of these two processes.  More
importantly, this might allow us to define joint models that describe how
mobile users behave from both a social and spatial point of view. 

% Migration and friendship ties?
The close inter-dependence  between user mobility and 
social connections becomes even more compelling when considering long-range social
connections, spanning large distances even across continents. One could posit
that such ties were created when users were in direct spatial proximity at some
point in the past; then, one of the two parties migrated somewhere else,
effectively creating a long-range social connection. This would imply that a
more meaningful explanation of the geographic patterns of social interaction
could lie in individual migration patterns, spanning short and long
distances and ranging from daily movements to long-term relocation shifts. A
recent study by Levy discusses how such migration patterns exhibit
statistical regularities that could explain the observed effect of geographic
distance on social connections~\cite{Lev10:migration}. More data and more
studies in this direction could help shed more light on this initial insight.


\section{Outlook}
The importance that spatial proximity holds in connecting people together has
been recently exploited by a new generation of mobile applications  that use
location-sensing technology available in modern devices to continuously acquire
data about other users nearby. Mobile applications such as
Highlight\furl{highlig.ht}, Banjo\furl{ban.jo}, Sonar\furl{www.sonar.me} and
Glancee\furl{www.glancee.com} help users discover new friends by matching
geographically close users according to their shared interests and
personal profiles.  These new services seem to pave the way for a broader trend:
location data will be increasingly available on online services and ingrained
in the features they offer. As powerful mobile devices become mainstream, the
potential audience of location-based services could easily grow as online
social services did over the last years, changing the Web  yet again.

Overall, this dissertation has made a step in addressing
how the spatial properties of online social networks can be used effectively 
to understand and model their structure and to design and deploy related
systems. As location-based data will be increasingly more available, our
findings and results open the door to a vast range of future possibilities. Our
results are relevant both to researchers and to practitioners: the former would
benefit from these insights when studying online social services, while the latter
could be aware of these additional possibilities when building systems
and applications related to online social platforms.

Despite the clear effect that space and geography have on online users,  we
imagine that taking advantage of the spatial properties of social services 
in real scenarios would still present interesting design challenges. Facing
these challenges requires inventive thinking and technical knowledge that stem from the particular
domain of interest: our hope is that this work and its results can facilitate
and inspire such creative process, by offering a new perspective on online
social services.



